With the advent of digital images and digital image distributions protection of such digital images against unauthorised copying has become an issue for image publishers and authors One technique used to identify the ownership of an image is to embed a pattern or patterns into the image, such that the embedded pattern is not visible to the naked eye of an observer. Such a pattern is called a watermark. The presence of the watermark can be detected in the copied image by the owner of the original image, thereby proving their ownership.
Systems are known for embedding a pattern or patterns into an image or document. However, present methods of invisible watermarking of documents and images are often very sensitive, therefore not robust, to geometric image distortions. The most common image distortions are changes in the magnification or scaling, changes to the orientation of the image or rotation, and losing edge information of the image or cropping.
Known methods which are robust to such changes, are either incapable of storing significant amounts of data in the watermark, or are susceptible to malicious intervention for the reason that the pattern is easily detected by simple spectral methods. One such spectral method is an analysis of the Fourier magnitude peaks of the image with an embedded watermark.
One of the most popular and effective methods for detecting patterns is correlation. In fact, for linear systems, correlation, or matched filtering, can be shown to be mathematically an optimal detection method. Unfortunately correlation in two dimensions is not, in general, invariant with orientation or scaling.
It should be noted that correlation can only give well defined and easily distinguished correlation magnitude peaks if the underlying pattern has a broad Fourier magnitude distribution. This is a consequence of the uncertainty principle. Therefore, patterns with very sharp or constrained Fourier magnitudes, such as a narrow-bandpass function, are ill equipped for correlation purposes.
Rotation invariance in known systems is typically achieved by using circular symmetric patterns. Alternatively the correlation can be repeated many times with the test pattern at many different orientations, so that at least one correlation is close to the actual orientation. Scale related problems are usually solved by repeated correlations at many different scales so that at least one correlation is close to the actual scale. Such methods are impractical, and as a consequence correlation seldom is used in cases when arbitrary rotation and/or scaling is present.